Is she sinful for seeking the help of a man to carry her heavy items in a public place due to the unavailability of other help, and to avoid back pain, while committing to not speaking with men?

Your family is mistaken in their insistence on your education in a mixed-gender environment and your traveling alone without a mahram. This is a dereliction of their duty towards those under their care. Your insistence on leaving your studies in this mixed environment and avoiding speaking with non-mahram men is commendable. As for a non-mahram man helping you carry things, there is no harm in it, provided you are careful not to let this lead to familiarization. If you can convince your family to have a mahram accompany you on your travels, that would be best to avoid carrying things and traveling without a mahram. Otherwise, fear Allah as much as you are able.